Title: Fundamentals of Physics
1Fundamentals of Physics
- Chapter 8 Potential Energy Conservation of
Energy - Potential Energy
- Path Independence of Conservative Forces
- Determining Potential Energy Values
- Conservation of Mechanical Energy
- Reading a Potential Energy Curve
- Work Done on a System by an External Force
- Conservation of Energy
- Review Summary
- Questions
- Exercises Problems
2 Potential Energy
- Potential Energy is energy that can be
associated with the configuration of a system of
objects that exert forces on one another. - Gravitational Potential Energy
- Elastic Potential Energy
Chapter 6 - Kinetic Energy - state of motion
of objects in a system.
3Gravitational Potential Energy
Gravitational potential energy energy in a set
of separated objects which attract one another
via the gravitational force.
the system earth barbell
Increased P.E.
4Elastic Potential Energy
Elastic potential energy energy in a compressed
or stretched spring-like object.
e.g. Elastic potential energy stored in a dart
gun.
5Work Potential Energy
The change in the gravitational potential energy,
U, is defined to equal the negative of the work
done by the gravitational force, Wg.
DU - Wg
6Work done by Gravity
leaves at 1.20 m max h 4.80 m what is v0
7Conservative Nonconservative Forces
- Conservative Force Example
- Spring Force
W1 - W2
W1 Negative Work done by the spring
An important concept!
Negative Work done by friction
- Nonconservative Force Example
- Friction Force
W2 Positive Work done by the spring
Negative Work done by friction
8Work Done by Gravity on a Closed Path
9Work Done by Friction on a Closed Path
10Conservative Forces
- Work done by the gravitation force does not
depend upon the choice of paths a conservative
force. - Definition of a Conservative Force
- Version 1 A force is conservative when the work
it does on a moving object is independent of the
path between the objects initial and final
position. - Version 2 A force is conservative when it does
no net work on an object moving around a closed
path, starting and finishing at the same point
11Path Independence of Conservative Forces
Consider a particle moving under the influence of
a conservative force then
Wab - Wba
Furthermore
The work done by a conservative force on a
particle moving between two points does not
depend on the path taken by the particle.
The net work done by a conservative force on a
particle moving around every closed path is zero
Wab,1 Wba,2 0
Wab,1 Wab,2
12Determining Potential Energy Values
The change in the potential energy is defined to
equal the negative of the work done by the forces
in the system
DU - W
Only changes in the potential energy of an object
are related to work done by forces on the object
or to changes in its kinetic energy hence, the
reference point at which U 0 is arbitrary and
can be conveniently chosen.
Work done by a general variable force (Sec. 7-6)
Hence
13Gravitational Potential Energy Values
Gravitational potential energy energy in a set
of separated objects which attract one another
via the gravitational force.
the system earth barbell
14Elastic Potential Energy Values
If U0 at the relaxed length
15Conservation of Mechanical Energy
16Conservation of Mechanical Energy
Work-KE Theorem
Definition
Total Mechanical Energy
Total Mechanical Energy is conserved.
17Conservation of Mechanical Energy
Cutnell p 168
18Example Energy is conserved
19An Alternative to Newtons Laws
Solve using vector forces and kinematics.
Easier to solve using conservation of energy.
(frictionless surfaces)
20Solving a Kinematics Problem Using Conservation
of Energy
21Graduation Fling
m 0.120 kg vi 7.85 m/s v at 1.18 m ?
22Speed Is Independent of Path
23Catching a Home Run
m .15 kg vi 36 m/s H 7.2 m KE when
caught Speed when caught
24Who is faster at the bottom?
25Skateboard Exit Ramp
M 55 kg vi 6.5 m/s vf 4.1 m/s h ?
26What is the final speed?
Snowboarder starts at 4 m/s, v 0 at
top Snowboarder starts at 5 m/s, v ?
27Find the Speed of the Block
m 1.70 kg k 955 N/m Compressed 4.60 cm v at
equilibrium position
28Reading a Potential Energy Curve
Consider the energy of a particle subject to an
elastic force
29Reading a Potential Energy Curve
A particle subject to a conservative force e.g.
an elastic force
The total mechanical energy of the particle is a
constant.
30Reading a Potential Energy Curve
31Reading a Potential Energy Curve
Equilibrium F 0 and K 0 Stable
x2 and x4 Unstable x3 Neutral to the
right of x5
free to leave
trapped
trapped
32Work Done on a System by an External Force
Work is energy transferred to or from a system by
means of an external force acting on that system.
W DEmec DK DU
Lifting the bowling ball
changes the energy of the earth-ball system.
33Work Done on a System by an External Force
(Thermal Energy)
- Work change in motion heat
(e.g. rubbing your hands together)
Generalizing
34Non-Conservative Forces
- What are some non- conservative forces?
- frictional forces
- air resistance
W Wc Wnc -DU Wnc DK Wnc DU DK Wnc
DE
- Summary
- Wtotal DK
- Wc - DU
- Wnc DE
35Conservation of Energy
The total energy of a system can change only by
amounts of energy that are transferred to or from
the system. W D E D Emec D Eth
D Eint The total energy of an isolated system
cannot change. D E D Emec D Eth D
Eint 0 In an isolated system, we can relate
the total energy at one instant to the total
energy at another instant without considering the
energies at intermediate times.
36Conservation of Energy
Roller coaster without friction as an isolated
system D Emec D Eth D Eint 0
Emec ½ m v2 mgh constant At
Point A ½ m v02 mgh ½ m vA2 mgh
constant At Point B ½ m v02 mgh
½ m vB2 mg(h/2) At Point C ½ m v02
mgh ½ m vC2
37Drop a Textbook
Drop a 2 kg textbook
- Wg
- DUgp
- U10
- U1.5
- Wg
- DU
- U10
- U1.5
If U0 100 J
38Pendulum Problem
- bob has a speed v0 when the cord makes an angle
q0 with the vertical. - Find an expression for speed of the bob at its
lowest position - Least value of v0 if the bob is to swing down and
then up to - Horizontal position
- Straight up vertically
39Skier
60 kg skier starts at rest at a height of 20.0 m
above end of a ski jump ramp. As skier leaves
ramp, velocity is at an angle of 280 with
horizontal. Maximum height? With backpack of
mass 10 kg?
40Find the Divers Depth
m 95.0 kg h 3.0 m Wnc -5120 J d ?
41Nonconservative Forces
Wnc (½ mvf2 mghf ) - ( ½ mvo2 mgh0)
0.20 kg rocket hf - h0 29 m 425 J of work is
done by propellant vf ?
42A Potential Problem
m 1.60 kg At x 0, v 2.30 m/s v at x 2.00
m ?